Rewrite as a simplified fraction. ${2.53\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2536.6666...\\ 100x &= 253.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2283}$ ${x = \dfrac{2283}{900}} $ ${x = \dfrac{761}{300}} \text{or} {2 \dfrac{161}{300}}$